Bucknell held Arizona in check, leading by as many as 13 in the first half. The Wildcats briefly took at two-point lead in the second half, but Bucknell held Arizona to 35 percent shooting for the game.
"The bar is set high and we relish those expectations, we didn't want any moral victories," said Bucknell coach Dave Paulsen.
The Wildcats never appeared fully ready to play, which coach Sean Miller attributed to coming off a disappointing loss in the Pac 12 championship game.
"I don't know if we entered today's game not really over the Pac 12 Tournament, and if you don't put that behind you, you will lose to a really good team, and that's what happened tonight," said Miller.
Solomon Hill led the Wildcats (23-12) with 17 points and nine rebounds, and senior Jesse Perry added 14 points.
Arizona, which fell to 0-4 all-time in the tournament, hadn't made an appearance in the NIT since 1951.
"The NIT should have been an opportunity that we looked forward to," said junior Solomon Hill. "Preparation going into the game didn't go as well and smooth as it should have. It happens. There is good competition out there. We had all the chance, it just didn't come down our way."
In other first-round games:
* At Coral Gables, Fla., Rion Brown scored 18 points to lead Miami to a 66-50 win over Valparaiso. The Hurricanes stretched a four-point lead and finished the game with a 16-0 run over the final 3:41. Malcolm Grant and Shane Larkin keyed the run with consecutive three-pointers.
Larkin scored 12 points and Trey McKinney Jones finished with 10 for Miami (20-12).
Ryan Broekhoff had 18 points and Richie Edwards added 16 for the Crusaders (22-12).
Miami advances to a second-round matchup Sunday against Minnesota.
* At Tulsa, Dario Hunt had 18 points and 10 rebounds to lead Nevada past Oral Roberts, 68-59.
Deonte Burton added 17 points as the Wolf Pack (27-6) advanced to a second-round matchup against Bucknell.
Burton, Olek Czyz and Malik Story each had eight points in the second half to help rally Nevada, which trailed 30-29 at halftime.
Dominique Morrison and Rod Pearson had 13 points apiece for the Golden Eagles (27-7), who were outrebounded 45-29.
Oral Roberts led 50-49 before Czyz scored with 8:03 left to ignite Nevada's decisive 8-0 run. Burton sank three free throws with 2:10 left to stretch Nevada's lead to 62-55 and the Golden Eagles never got any closer.
* At Oxford, Miss., Tyler Brown scored 26 points, Nic Moore added 24 and Illinois State put on record-setting shooting display in a 96-93 overtime victory over Mississippi.
Illinois State (21-13) set a Tad Smith Coliseum record for three-pointers, making 17 of 23 (73.9 percent) from beyond the arc.
Brown was 8-for-9 from three-point range, while Moore made all six of his attempts.
LaDarius White scored 25 points and Terrance Henry added 21 for Ole Miss (20-14), which lost in the NIT's first round for the second straight season.
Brown put Illinois State up 61-49 after his seventh three-pointer with 12:22 remaining in regulation and it looked as if the Redbirds would cruise, but Ole Miss rallied to tie it at 84 and Jarvis Summers just missed a 10-foot jumper at the buzzer to send it to overtime.